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Nesting order for mixed models

2 messages · Jon Zadra, Douglas Bates

Jon Zadra
# 
Hello,

I am confused about the order of nesting in mixed models using functions 
like aov(), lme(), lmer().

I have the following data:
n subjects in either condition A or B
each subject tested at each of 3 numerical values ("distance" = 
40,50,60), repeated 4 times for each of the 3 numerical values ("trial" 
= 1,2,3,4)

Variable summary:
Condition: 2 level factor
Distance: numerical (but only 3 values) in the same units as "y"
Trial: 4 level factor

I expect the subjects' data to differ due to condition and distance, and 
am doing repeated measurements to reduce any variability due to 
measurement error.

Currently I'm using this model:

lme(y ~ Condition + Distance, random = ...)

the question is how do I organize the random statement?  Is it:
random = ~1 | Subject
random = ~1 | Subject/Trial
random = ~1 | Trial/Subject
random = ~1 | Condition/Distance/Subject/Trial
...etc, or something else entirely?

Mostly I'm unclear about whether the Trials should be grouped under 
subject because I expect the trials to be more similar within a subject 
than across subjects, or whether subjects should be grouped under trials 
because the trials are going to differ depending on the subject.  If 
trials should be grouped under subjects, then do the condition or 
distance belong as well, since the trials will be most similar within 
each distance within each subject?

Thanks in advance!

- Jon
Douglas Bates
#
On Tue, Mar 10, 2009 at 2:47 PM, Jon Zadra <jrz9f at virginia.edu> wrote:
I don't think Trial is necessary.  If I understand correctly it is not
really an experimental or observational factor in that you don't
expect that trial 1 for one subject/distance combination will be
related to trial 1 for another combination.
I think that is all you need.   In lmer the formula would be y ~
Condition + Distance + (1|Subject).
In some ways of thinking of the model, Trial would be grouped under
the Subject:Distance combination but then it becomes unnecessary
because it is just another way of labeling the observations.  A random
effect for Trial within Subject:Distance is confounded with the
"residual" or per-observation noise term.